If the Hubble telescope were aimed at the Earth, how detailed would the images be?

—Kyle Rankin

This is a common question. The Hubble operators get it a lot, and their
FAQ page answers
it.
The problem isn’t—as some people say—that the Earth is too bright. As
Phil Plait of Bad Astronomy pointed
out, Hubble
looks at Earth pretty regularly.

The real problem is that Hubble is moving over the surface at over 7
kilometers per second. Even a short exposure would be a blur.

That’s no fun. Is there a way we could make it work? I decided to take a
closer look.

As our picture target, we’ll use this typical desk:

The Earth’s atmosphere won’t be a problem. It’s actually much more of a
problem for surface-based telescopes looking at space than for
space-based telescopes looking at the surface. The reason for this is
geometric:

Hubble is the best visible-light telescope we have, but its resolution
does have limits. Pluto, out in the Kuiper belt, lies right at those
limits. The best pictures we have of
Pluto come
from Hubble, but the ex-planet is still little more than a mysterious
blur.

At that resolution (about 0.05 arcseconds, give or take) and Hubble’s
distance from the desk (about 570 kilometers) the desk would look like
this:

But that desk is also zooming by, so even a perfect image will be
blurred:

Combining the two effects gives us an end result that looks like this:

That’s no good.

Could we rotate Hubble to track the surface, and eliminate the blur?

Hubble swivels to follow targets. Usually, they’re far enough away that
we can assume they’re at infinite distance. The automatic on-board
parallax algorithms can’t handle targets closer than about ten times the
distance to the Moon. When astronomers want to use it to take pictures
of the Moon, sometimes they send it commands to rotate
manually,
then turn on the camera mid-maneuver.

It doesn’t work very well. Moving Hubble at those speeds is cumbersome
with the current guidance package. The resulting
photos are
better than what you can see with the naked eye, but they’re not very
good by Hubble standards. Here’s our desk, with the image degraded by a
similar amount that the Moon one was:

Fortunately, the Moon is bright enough that if you’ll settle for a short
exposure, you can avoid the problem. This
photo was
taken with a half-second exposure, short enough that it didn’t have to
do much in the way of tracking.

Unfortunately, our desk is moving across the telescope’s field of view
about 600 times faster than the Moon. Tracking is unavoidable.

The strange thing is, the desk really isn’t moving all that fast. Hubble
is just really slow. To track the surface, it would need to rotate less
than a degree per second at maximum.

But Hubble wasn’t built for surface tracking. The telescope’s top
rotational (“slew”) speed is only a few degrees per minute (about the
speed of a minute hand on a clock) and even those speeds are fast enough
that its gyroscopes cause it to
vibrate,
which destroys the image quality.

Clearly, we’d need to disable Hubble’s guidance system and bolt on our
own control system. Hubble’s rotational moment of
inertia is
similar to that of a small carousel; too hard for the existing
gyroscopes to move, but not hard in the absolute sense. With our custom
control system, it could be made to track the surface, and get photos
pretty close to optimal quality:

But this isn’t just a hypothetical situation.

Much of the technology in military spy satellites is believed to be
similar to that of Hubble. So in a sense, pointing a Hubble-type
telescope at the surface is not only possible—it’s what the US
government actually does.